Galois category

Summary

A Galois category is a category with a functor to finite sets, called a fibre functor. The pair satisfies axioms modelled on finite covering spaces and on finite separable field extensions. The main theorem says that such a category is equivalent to the category of finite sets with a continuous action of a profinite group. This group is the automorphism group of the fibre functor. It is the abstract frame of Grothendieck's Galois theory. With finite étale covers of a connected scheme it defines the étale fundamental group.